Механика

$F = ma$

$A = Fs\cos\alpha$

$A_x=A\cos\alpha$

$A=\sqrt{A_x^2+A_y^2}$

$\vec v=\vec v' + \vec u$

$v=\frac{2\pi R}{T}$

$\omega=\frac{2\pi}{T}=2\pi\nu$

$a_c=\frac{v^2}{R}=\omega^2R$

$F_c=m\frac{v^2}{R}=m\omega^2R$

$F=G\frac{m_1m_2}{r^2}$

$g=G\frac{M}{R^2}$

$v_1=\sqrt{\frac{GM}{R}}=\sqrt{gR}$

$v=\frac{s}{t}$

$s=v\cdot t$

$t=\frac{s}{v}$

$F_{\text{тяж}}=mg$

$A=F\cdot s$

$P=\frac{A}{t}$

$a=\frac{v-v_0}{t}$

$v=v_0+at$

$s=v_0t+\frac{at^2}{2}$

$x=x_0+v_0t+\frac{at^2}{2}$

$v^2-v_0^2=2as$

$p=mv$

$J=F\Delta t=\Delta p$

$m_1v_1+m_2v_2=m_1u_1+m_2u_2$

$E_k=\frac{mv^2}{2}$

$E_k+E_p=\text{const}$

$L=T-U$

$\frac{d}{dt}\frac{\partial L}{\partial \dot q_i}-\frac{\partial L}{\partial q_i}=Q_i^{(nc)}$

$p_i=\frac{\partial L}{\partial \dot q_i}$

$H(q,p,t)=\sum_i p_i\dot q_i-L(q,\dot q,t)$

$\dot q_i=\frac{\partial H}{\partial p_i},\quad \dot p_i=-\frac{\partial H}{\partial q_i}$

$\frac{df}{dt}=\{f,H\}+\frac{\partial f}{\partial t},\quad \{f,g\}=\sum_i\left(\frac{\partial f}{\partial q_i}\frac{\partial g}{\partial p_i}-\frac{\partial f}{\partial p_i}\frac{\partial g}{\partial q_i}\right)$

$U_{\text{eff}}(r)=U(r)+\frac{\ell^2}{2mr^2}$

$T_{rot}=\frac12\boldsymbol{\omega}^{T}I\boldsymbol{\omega}$

$I=I_{cm}+ma^2$

$\omega^2=\frac{U''(q_0)}{m_{eff}}$